1. Field of the Invention
The present invention relates to a position detecting method and unit, an optical characteristic measuring method and unit, an exposure apparatus, and a device manufacturing method, and more specifically to a position detecting method and unit for detecting the position of an image formed by an optical system, an optical characteristic measuring method and unit for measuring an optical characteristic of an optical system to be examined using the position detecting method, an exposure apparatus comprising the optical characteristic measuring unit, and a device manufacturing method using the exposure apparatus.
2. Description of the Related Art
In a lithography process for manufacturing semiconductor devices, liquid crystal display devices, or the like, exposure apparatuses have been used which transfer a pattern (also referred to as a xe2x80x9creticle patternxe2x80x9d hereinafter) formed on a mask or reticle (generically referred to as a xe2x80x9creticlexe2x80x9d hereinafter) onto a substrate, such as a wafer or glass plate (hereinafter, generically referred to as a xe2x80x9csubstratexe2x80x9d as needed), coated with a resist through a projection optical system. As such an exposure apparatus, a stationary-exposure-type projection exposure apparatus such as the so-called stepper, or a scanning-exposure-type projection exposure apparatus such as the so-called scanning stepper is mainly used.
Such an exposure apparatus needs to accurately project the pattern on a reticle onto a substrate with high resolving power. Therefore, the projection optical system is designed to have a good optical characteristic with various types of aberrations being reduced.
However, it is difficult to make a projection optical system completely as is planned in design, and various types of aberrations due to various factors remain in a projection optical system actually made. Therefore, the optical characteristic of the projection optical system actually made is not the same as planned in design.
Various technologies for measuring the optical characteristic, related to aberration, of the actually made projection optical system as an optical system to be examined have been suggested, and of those technologies a wave-front aberration measuring method is attracting attentions, which comprises (a) making a spherical wave produced by a pinhole incident on the optical system to be examined, (b) producing parallel rays of light from light that has passed through the optical system to be examined and forms a pinhole image and dividing the wave front thereof into a plurality of portions, (c) making each of the portions form a spot image, and (d) calculating wave-front aberration due to the optical system based on measured positions where the spot images are formed.
A wave-front aberration measuring unit using this method may comprise a micro-lens array, in which a plurality of micro lenses are arranged along a two-dimensional plane parallel to the ideal wave front of the parallel rays of light, as a wave-front dividing device for dividing the incident light and making each of the divided wave-front portions form a spot image. The wave-front aberration measuring unit picks up the spot images by a pick-up device such as CCD, calculates the center-of-gravity of light intensity of each spot-image using a center-of-gravity method or a position where correlation between light intensity distribution of each spot-image and a template is maximal using a correlation method, to detect the positions of the spot images, and calculates wave-front aberration based on deviations of the detected spot images"" positions from positions planned in design.
The center-of-gravity method and correlation method are robust to noise and generally an excellent method. However, in the case of detecting the positions of spot-images by a small number of picture elements (e.g., a 5xc3x975 matrix arrangement of effective picture elements) and with accuracy of much smaller than the dimension of the picture element (e.g., {fraction (1/100)} to {fraction (1/1000)} of the dimension of the picture element), they are not effective.
That is, the center-of-gravity method with a small number of picture elements cannot detect the positions of spot-images with desired accuracy in principle. Moreover, because the correlation method needs to calculate correlations with a very large number of templates (about 100xc3x97100 to 1000xc3x971000), it cannot quickly detect positions.
Because of the demand for further improved exposure accuracy corresponding to increasingly high integration in recent years, in measuring wave-front aberration due to a projection optical system, the method of detecting the positions of spot-images by a small number of picture elements and with accuracy of much smaller than the dimension of the picture element is needed.
This invention was made under such circumstances, and a first purpose of the present invention is to provide a position detecting method and unit which can quickly and accurately detect the positions of spot-images even by a small number of picture elements.
Moreover, a second purpose of the present invention is to provide an optical characteristic measuring method and unit which accurately detects the optical characteristic of an optical system to be examined.
Furthermore, a third purpose of the present invention is to provide an exposure apparatus that can accurately transfer a given pattern onto a substrate.
Moreover, a fourth purpose of the present invention is to provide a device manufacturing method which can manufacture highly integrated devices having a fine pattern thereon.
According to a first aspect of the present invention, there is provided a position detecting method with which to detect a position of a picked-up image, the position detecting method comprising preparing a plurality of templates with which correlation values of a picture-element data distribution, as a pick-up result of the image, are calculated and which correspond to same reference images of which center positions are spaced a predetermined distance apart; obtaining, by calculating correlation values between the picture-element data distribution and the plurality of templates, position of a maximum template whose correlation value is maximal; obtaining at least one of a curved line function and curved surface function which fit a distribution of correlation values of the correlation values calculated, the center of the distribution being present in the maximum template""s position; and calculating position of the picked-up image based on the at least one function.
According to this, correlation values between a plurality of templates prepared beforehand and a picture-element data distribution as a pick-up result of an image are calculated, and the position of a maximum template whose correlation value is the maximum of the calculated correlation values is obtained, the maximum template""s position being the center of a reference image in the template. At this point of time the position of the image is identified with accuracy of a predetermined distance which is adopted in generating the plurality of template. Subsequently, at least one of a curved line function and curved surface function is calculated which fits the distribution of calculated correlation-values in positions near the maximum template""s position and which is a function of position, and the position of the picked-up image is calculated based on the at least one function. A position where the at least one function takes on, e.g., a local maximum near the maximum template""s position is calculated as the position of the picked-up image. As a result, the position of the picked-up image can be detected with improved accuracy in comparison to the predetermined distance. Therefore, the number of templates prepared beforehand to achieve desired accuracy in detecting a position and the number of times of calculating correlation-values can be reduced, and the image position can be quickly and accurately detected.
In the position detecting method according to this invention, the picked-up image may be a spot image.
Moreover, in the position detecting method according to this invention, when a first number denoting the number of the correlation values to which the at least one function is fitted is larger than a second number denoting the number of parameters which define the at least one function, the second number of parameters may be determined using a statistical method to obtain the at least one function.
According to a second aspect of the present invention, there is provided a position detecting unit which detects a position of a picked-up image by a pick-up unit, the position detecting unit comprising a template-preparing unit connected to the pick-up unit, which prepares a plurality of templates with which correlation values of a picture-element data distribution, as a pick-up result of the image, are calculated and which correspond to same reference images of which center positions are spaced a predetermined distance apart; a correlation-computing unit connected to the template-preparing unit, which, by calculating correlation values between the picture-element data distribution and the plurality of templates, obtains position of a maximum template whose correlation value is maximal; and an image-position calculating unit connected to the correlation-computing unit, which obtains at least one of a curved line function and curved surface function which fit a distribution of correlation values of the correlation values calculated and each are a function of position, the center of the distribution being present in the maximum template""s position, and calculates position of the picked-up image based on the at least one function.
According to this, a correlation-computing unit calculates correlation values between a plurality of templates prepared beforehand by a template-preparing unit and a picture-element data distribution as a pick-up result of an image, and obtains the position of a maximum template whose correlation value is the maximum of the calculated correlation values. And an image-position calculating unit obtains at least one of a curved line function and curved surface function which fit the distribution of calculated correlation-values in positions near the maximum template""s position and calculates the position of the picked-up image based on the at least one function. That is, the position detecting unit according to this invention detects the position of an image by the position detecting method of this invention. Therefore, the image position can be quickly and accurately detected.
In the position detecting unit according to this invention, the picked-up image may be a spot image.
According to a third aspect of the present invention, there is provided an optical characteristic measuring method with which to measure an optical characteristic of an optical system to be examined, the optical characteristic measuring method comprising dividing a wave front of light which has passed through the optical system to be examined, to form a plurality of images; picking up the plurality of images; detecting positions of the plurality of images picked up in the picking-up using the position detecting method according to this invention; and calculating an optical characteristic of the optical system to be examined based on the detected positions of the images.
According to this, the positions of the plurality of images formed on the image plane are accurately detected using the position detecting method according to this invention. Based on the detected positions of the plurality of images, the optical characteristic of the optical system to be examined is calculated. Accordingly, the optical characteristic of the optical system can be very accurately measured.
In the optical characteristic measuring method according to this invention, the optical characteristic may be wave-front aberration.
According to a fourth aspect of the present invention, there is provided an optical characteristic measuring unit which measures an optical characteristic of an optical system to be examined, the optical characteristic measuring unit comprising a wave-front dividing device which is arranged on an optical path of light passing through the optical system to be examined, divides a wave front of the light passing through the optical system to be examined, and forms a plurality of images; a pick-up unit which is arranged a predetermined distance apart from the wave-front dividing device and picks up the plurality of images; a position detecting unit according to claim 4, which is connected to the pick-up unit and detects positions of the plurality of images picked up by the pick-up unit; and an optical characteristic calculating unit connected to the position detecting unit, which calculates an optical characteristic of the optical system to be examined based on the detected positions of the plurality of images.
According to this, a pick-up unit picks up a plurality of images that is formed through a wave-front dividing device. Subsequently, a position detecting unit using the position detecting method of this invention accurately detects the positions of the plurality of images from the pick-up result. And an optical characteristic calculating unit calculates the optical characteristic of the optical system to be examined based on the detected positions of the plurality of images. That is, the optical characteristic measuring unit of this invention measures the optical characteristic of the optical system to be examined using the optical characteristic measuring method of this invention, so that the optical characteristic of the optical system can be accurately measured.
In the optical characteristic measuring unit according to this invention, the wave-front dividing device may be a micro-lens array in which lens elements are arranged two-dimensionally.
Moreover, in the optical characteristic measuring unit according to this invention, the optical system to be examined may be a projection optical system that transfers a pattern formed on a mask onto a substrate.
According to a fifth aspect of the present invention, there is provided an exposure apparatus which, by illuminating a substrate with exposure light, transfers a predetermined pattern onto a substrate, comprising an exposure apparatus main body which comprises a projection optical system arranged on an optical path of the exposure light; and an optical characteristic measuring unit according to this invention with the projection optical system as the optical system to be examined.
According to this, a given pattern is transferred on a substrate by a projection optical system of which the optical characteristic has been measured accurately by the optical characteristic measuring unit of this invention and adjusted suitably. Therefore, the given pattern can be very accurately transferred on the substrate.
In the exposure apparatus according to this invention, the optical characteristic measuring unit may be attachable to and detachable from the exposure apparatus main body.
According to a sixth aspect of the present invention, there is provided a device manufacturing method including a lithography process, wherein in the lithography process, an exposure apparatus according to this invention performs exposure. According to this, because the exposure apparatus of this invention can very accurately transfer a given pattern onto divided areas, productivity in manufacturing highly integrated devices having a fine circuit pattern can be improved.